Let X and Y be independent exponential random variables with respective rates λ and μ, where λ >… 1 answer below »

Let X and Y be independent exponential random variables with respective rates λ and μ, where λ > μ. Let c > 0.

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(a) Show that the conditional density function of X, given that X +Y = c, is

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(b) Use part (a) to find E [X|X +Y = c].

(c) Find E [Y|X +Y = c].

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